Do I have to create new form?
Yes, You have to create a new content type based on free object
——-
After I chose Name in form A I cannot use the same again in form B and my exported databases have to look like Name1, Name2 etc.
I had to study the database to really understand what was going on.
There are three tables any article will use:
#__content - joomla table
#__cck_store_item_content (this is extra table for all content types based on article)
#__cck_store_form_something - fields specific and only for this content type
If you want to reuse fields for all articles, then padlock for field needs to be open when you create it